A331309 a(n) = A000005(A225546(n)), where A000005 gives the number of divisors of n.

1, 2, 3, 2, 5, 4, 9, 4, 3, 6, 17, 6, 33, 10, 7, 2, 65, 6, 129, 10, 11, 18, 257, 8, 5, 34, 9, 18, 513, 8, 1025, 4, 19, 66, 13, 4, 2049, 130, 35, 12, 4097, 12, 8193, 34, 15, 258, 16385, 6, 9, 10, 67, 66, 32769, 12, 21, 20, 131, 514, 65537, 14, 131073, 1026, 27, 4, 37, 20, 262145, 130, 259, 14, 524289, 8, 1048577, 2050, 15

Offset: 1

Author

Antti Karttunen, Jan 21 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A048675, A225546, A331287, A331308, A331591.

Programs

PARI

A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
A331309(n) = if(1==n,1,my(f=factor(n),u=#binary(vecmax(f[, 2])),prods=vector(u,x,1),m=1,e); for(i=1,u,for(k=1,#f~, if(bitand(f[k,2],m),prods[i] *= f[k,1])); m<<=1); prod(i=1,u,1+A048675(prods[i])));

Formula

a(n) = A000005(A225546(n)).